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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2016 Volume 453, Pages 198–218 (Mi znsl6379)

This article is cited in 8 papers

On functionals dual to minimal splines

A. A. Makarov

St. Petersburg State University, St. Petersburg, Russia

Abstract: The paper considers minimal splines of Lagrange type of lower orders, and a system of functionals biorthogonal to the system of minimal coordinate splines is constructed. The results obtained are illustrated on the example of a polynomial generating vector function, which leads to the construction of $B$-splines from the approximation relations.

Key words and phrases: minimal spline, $B$-spline, biorthogonal system, dual functional, de Boor–Fix functional.

UDC: 519.6

Received: 11.10.2016


 English version:
Journal of Mathematical Sciences (New York), 2017, 224:6, 942–955

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© Steklov Math. Inst. of RAS, 2025